Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2925 conjugacy classes of subgroups.
The subgroup lattice has 748 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #11722676 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | #11722639 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #41×(C3⋊D3)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | Q8×((C3⋊D3)⋊C3)⋊C2 | C2 | 1 | 2 | yes | maximal, complemented |
| 5 | #11722516 | C2 | 1 | 2 | yes | maximal, complemented |
| 6 | #11722504 | C2 | 1 | 6 | yes | maximal, complemented |
| 7 | #11722502 | C2 | 1 | 6 | yes | maximal, complemented |
| 8 | #11722490 | C2 | 1 | 3 | yes | maximal, complemented |
| 9 | #11722483 | C2 | 1 | 3 | yes | maximal, complemented |
| 10 | #11722482 | C2 | 1 | 3 | yes | maximal, complemented |
| 11 | C2×((C3⋊D3)⋊C3)⋊Q8 | C2 | 1 | 3 | yes | maximal, complemented |
| 12 | #10596694 | — | 3 | 1 | no | maximal |
| 13 | D3×#1010 | — | 3 | 1 | no | maximal |
| 14 | #41×H(3,𝔽3) | C22 | 1 | 1 | yes | characteristic, complemented |
| 15 | Q8×#272 | C22 | 1 | 2 | yes | complemented |
| 16 | #88744 | C22 | 1 | 6 | yes | complemented |
| 17 | #88740 | C22 | 1 | 3 | yes | complemented |
| 18 | C2×#6229 | C22 | 1 | 3 | yes | complemented |
| 19 | #88722 | C22 | 1 | 1 | yes | characteristic, complemented |
| 20 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 21 | Q8×(C3⋊D3)⋊C3 | C22 | 1 | 2 | yes | complemented |
| 22 | #3830⋊C3 | C22 | 1 | 3 | yes | complemented |
| 23 | #3830⋊C3 | C22 | 1 | 6 | yes | complemented |
| 24 | D4×(C3⋊D3)⋊C3 | C22 | 1 | 3 | yes | — |
| 25 | #3828⋊C3 | C22 | 1 | 3 | yes | complemented |
| 26 | #3828⋊C3 | C22 | 1 | 3 | yes | complemented |
| 27 | C2×C4×(C3⋊D3)⋊C3 | C22 | 1 | 3 | yes | — |
| 28 | C2×#634⋊C3 | C22 | 1 | 3 | yes | complemented |
| 29 | #88676 | C22 | 1 | 6 | yes | — |
| 30 | #88672 | C22 | 1 | 12 | yes | complemented |
| 31 | #88671 | C22 | 1 | 6 | yes | complemented |
| 32 | #88671 | C22 | 1 | 12 | yes | complemented |
| 33 | C2×((C3⋊D3)⋊C3)⋊C4 | C22 | 1 | 6 | yes | — |
| 34 | C2×#6196 | C22 | 1 | 6 | yes | complemented |
| 35 | #88654 | C22 | 1 | 1 | yes | characteristic |
| 36 | C4×((C3⋊D3)⋊C3)⋊C2 | C22 | 1 | 6 | yes | — |
| 37 | #88652 | C22 | 1 | 3 | yes | complemented |
| 38 | #88651 | C22 | 1 | 6 | yes | complemented |
| 39 | #88650 | C22 | 1 | 6 | yes | complemented |
| 40 | #88649 | C22 | 1 | 6 | yes | complemented |
| 41 | #88648 | C22 | 1 | 6 | yes | complemented |
| 42 | #88648 | C22 | 1 | 3 | yes | complemented |
| 43 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 6 | yes | — |
| 44 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 3 | yes | — |
| 45 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 46 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 47 | ((C3⋊D3)⋊C3)⋊Q8 | C22 | 1 | 6 | yes | complemented |
| 48 | #64367 | D3 | 1 | 1 | yes | characteristic, complemented |
| 49 | #41×C3⋊D3 | D3 | 1 | 1 | yes | characteristic, complemented |
| 50 | C3×#1010 | — | 3 | 1 | no | — |
| 51 | C3×#1010 | — | 3 | 1 | no | — |
| 52 | C3×#1010 | — | 3 | 1 | no | — |
| 53 | C3×#1010 | — | 6 | 1 | no | — |
| 54 | C3×D3×#41 | — | 3 | 1 | no | — |
| 55 | D32×Q8 | — | 3 | 2 | no | — |
| 56 | D32×Q8 | — | 3 | 2 | no | — |
| 57 | #64316 | — | 3 | 2 | no | — |
| 58 | #64315 | — | 3 | 2 | no | — |
| 59 | #64312 | — | 3 | 6 | no | — |
| 60 | D3×#237 | — | 3 | 6 | no | — |
| 61 | #64309 | — | 3 | 6 | no | — |
| 62 | #64309 | — | 3 | 6 | no | — |
| 63 | #64306 | — | 3 | 3 | no | — |
| 64 | D3×#235 | — | 3 | 3 | no | — |
| 65 | C2×#3797 | — | 3 | 3 | no | — |
| 66 | #64298 | — | 3 | 3 | no | — |
| 67 | #64297 | — | 3 | 3 | no | — |
| 68 | #64297 | — | 3 | 3 | no | — |
| 69 | #64297 | — | 3 | 3 | no | — |
| 70 | C2×D3×Dic6 | — | 3 | 3 | no | — |
| 71 | C22×(C3⋊D3)⋊C3 | C23 | 1 | 3 | yes | — |
| 72 | C2×((C3⋊D3)⋊C3)⋊C2 | C23 | 1 | 2 | yes | — |
| 73 | Q8×H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 74 | D4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 75 | C2×C4×H(3,𝔽3) | C23 | 1 | 3 | yes | — |
| 76 | #6235 | C23 | 1 | 6 | yes | — |
| 77 | C2×#1084 | C23 | 1 | 6 | yes | — |
| 78 | C4⋊#272 | C23 | 1 | 1 | yes | characteristic |
| 79 | C4×#272 | C23 | 1 | 6 | yes | — |
| 80 | #6229 | C23 | 1 | 3 | yes | — |
| 81 | #6229 | C23 | 1 | 6 | yes | — |
| 82 | #638⋊C3 | C23 | 1 | 6 | yes | — |
| 83 | #638⋊C3 | C23 | 1 | 6 | yes | — |
| 84 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 3 | yes | — |
| 85 | C2×(C3⋊Dic3)⋊C3 | C23 | 1 | 6 | yes | — |
| 86 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 1 | yes | characteristic |
| 87 | C4⋊((C3⋊D3)⋊C3) | C23 | 1 | 3 | yes | — |
| 88 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 1 | yes | characteristic |
| 89 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 3 | yes | — |
| 90 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 3 | yes | — |
| 91 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 3 | yes | — |
| 92 | C4×(C3⋊D3)⋊C3 | C23 | 1 | 6 | yes | — |
| 93 | #634⋊C3 | C23 | 1 | 3 | yes | — |
| 94 | #634⋊C3 | C23 | 1 | 6 | yes | — |
| 95 | #634⋊C3 | C23 | 1 | 3 | yes | — |
| 96 | #6200 | C23 | 1 | 6 | yes | — |
| 97 | #6200 | C23 | 1 | 2 | yes | — |
| 98 | #6199 | C23 | 1 | 6 | yes | — |
| 99 | #6198 | C23 | 1 | 6 | yes | — |
| 100 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 6 | yes | — |
| 101 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 12 | yes | — |
| 102 | ((C3⋊D3)⋊C3)⋊C4 | C23 | 1 | 6 | yes | — |
| 103 | #6196 | C23 | 1 | 6 | yes | — |
| 104 | #6196 | C23 | 1 | 12 | yes | — |
| 105 | D3×2−1+4 | — | 9 | 1 | no | — |
| 106 | D3×2−1+4 | — | 9 | 1 | no | — |
| 107 | C2×#1010 | — | 9 | 1 | no | — |
| 108 | C32×#41 | — | 2 | 1 | no | — |
| 109 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 110 | C32×#41 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 111 | #3832 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 112 | Q8×C3⋊D3 | C2×D3 | 1 | 1 | yes | characteristic |
| 113 | Q8×C3⋊D3 | C2×D3 | 1 | 2 | yes | complemented |
| 114 | #3830 | C2×D3 | 1 | 3 | yes | complemented |
| 115 | #3830 | C2×D3 | 1 | 6 | yes | complemented |
| 116 | D4×C3⋊D3 | C2×D3 | 1 | 3 | yes | — |
| 117 | #3828 | C2×D3 | 1 | 3 | yes | complemented |
| 118 | #3828 | C2×D3 | 1 | 3 | yes | complemented |
| 119 | C2×C4×C3⋊D3 | C2×D3 | 1 | 3 | yes | — |
| 120 | C2×#634 | C2×D3 | 1 | 3 | yes | complemented |
| 121 | C3×#239 | — | 3 | 1 | no | — |
| 122 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 123 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 124 | C3×D3×Q8 | — | 3 | 2 | no | — |
| 125 | C3×D3×Q8 | — | 3 | 1 | no | — |
| 126 | C3×D3×Q8 | — | 6 | 2 | no | — |
| 127 | C3×#237 | — | 3 | 3 | no | — |
| 128 | C3×#237 | — | 3 | 6 | no | — |
| 129 | C3×#237 | — | 3 | 6 | no | — |
| 130 | C3×#237 | — | 3 | 6 | no | — |
| 131 | C3×#237 | — | 6 | 6 | no | — |
| 132 | C3×D3×D4 | — | 3 | 3 | no | — |
| 133 | C3×#235 | — | 3 | 3 | no | — |
| 134 | C3×#235 | — | 3 | 3 | no | — |
| 135 | C3×#235 | — | 3 | 3 | no | — |
| 136 | C3×#235 | — | 3 | 3 | no | — |
| 137 | C3×#235 | — | 6 | 3 | no | — |
| 138 | C2×C3×C4×D3 | — | 3 | 3 | no | — |
| 139 | C2×C3×Dic6 | — | 3 | 3 | no | — |
| 140 | C2×C3×Dic6 | — | 3 | 3 | no | — |
| 141 | C2×C3×Dic6 | — | 3 | 3 | no | — |
| 142 | C2×C3×Dic6 | — | 6 | 3 | no | — |
| 143 | #3811 | — | 3 | 6 | no | — |
| 144 | D3×#67 | — | 3 | 6 | no | — |
| 145 | C2×#627 | — | 3 | 6 | no | — |
| 146 | C2×#627 | — | 3 | 6 | no | — |
| 147 | C2×#624 | — | 3 | 6 | no | — |
| 148 | #3805 | — | 3 | 12 | no | — |
| 149 | #3805 | — | 3 | 6 | no | — |
| 150 | #3804 | — | 3 | 12 | no | — |
| 151 | #3804 | — | 3 | 12 | no | — |
| 152 | #3804 | — | 3 | 12 | no | — |
| 153 | #3804 | — | 3 | 6 | no | — |
| 154 | C2×D3×Dic3 | — | 3 | 6 | no | — |
| 155 | #3802 | — | 3 | 1 | no | — |
| 156 | D3×D12 | — | 3 | 1 | no | — |
| 157 | C4×D32 | — | 3 | 6 | no | — |
| 158 | C4×D32 | — | 3 | 6 | no | — |
| 159 | #3799 | — | 3 | 3 | no | — |
| 160 | #3799 | — | 3 | 6 | no | — |
| 161 | #3799 | — | 3 | 6 | no | — |
| 162 | #3798 | — | 3 | 6 | no | — |
| 163 | #3798 | — | 3 | 6 | no | — |
| 164 | #3797 | — | 3 | 6 | no | — |
| 165 | #3797 | — | 3 | 6 | no | — |
| 166 | #3797 | — | 3 | 3 | no | — |
| 167 | #3797 | — | 3 | 6 | no | — |
| 168 | #3797 | — | 3 | 6 | no | — |
| 169 | #3796 | — | 3 | 3 | no | — |
| 170 | #3796 | — | 3 | 3 | no | — |
| 171 | #3796 | — | 3 | 6 | no | — |
| 172 | #3795 | — | 3 | 3 | no | — |
| 173 | #3795 | — | 3 | 6 | no | — |
| 174 | D3×Dic6 | — | 3 | 3 | no | — |
| 175 | D3×Dic6 | — | 3 | 6 | no | — |
| 176 | D3×Dic6 | — | 3 | 6 | no | — |
| 177 | D3×Dic6 | — | 3 | 6 | no | — |
| 178 | D3×Dic6 | — | 3 | 6 | no | — |
| 179 | D3×Dic6 | — | 3 | 6 | no | — |
| 180 | D3×Dic6 | — | 3 | 6 | no | — |
| 181 | C22×H(3,𝔽3) | C24 | 1 | 3 | yes | — |
| 182 | C2×#272 | C24 | 1 | 2 | yes | — |
| 183 | C2×(C3⋊D3)⋊C3 | — | 2 | 6 | no | — |
| 184 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 3 | yes | — |
| 185 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 2 | yes | — |
| 186 | C2×(C3⋊D3)⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 187 | ((C3⋊D3)⋊C3)⋊C2 | — | 2 | 4 | no | — |
| 188 | C4×H(3,𝔽3) | C24 | 1 | 1 | yes | characteristic |
| 189 | C4×H(3,𝔽3) | C24 | 1 | 3 | yes | — |
| 190 | #1084 | C24 | 1 | 6 | yes | — |
| 191 | (C3⋊Dic3)⋊C3 | C24 | 1 | 1 | yes | characteristic |
| 192 | (C3⋊Dic3)⋊C3 | C24 | 1 | 3 | yes | — |
| 193 | (C3⋊Dic3)⋊C3 | C24 | 1 | 6 | yes | — |
| 194 | C3×2−1+4 | — | 9 | 1 | no | — |
| 195 | C3×2−1+4 | — | 9 | 1 | no | — |
| 196 | C2×C3×#41 | — | 9 | 1 | no | — |
| 197 | #1010 | — | 3 | 1 | no | — |
| 198 | #1010 | — | 3 | 1 | no | — |
| 199 | #1010 | — | 3 | 1 | no | — |
| 200 | #1010 | — | 6 | 1 | no | — |
| 201 | #1010 | — | 9 | 1 | no | — |
| 202 | #1010 | — | 9 | 3 | no | — |
| 203 | #1010 | — | 9 | 3 | no | — |
| 204 | #1010 | — | 9 | 3 | no | — |
| 205 | #1010 | — | 9 | 3 | no | — |
| 206 | #1010 | — | 9 | 6 | no | — |
| 207 | #1010 | — | 9 | 6 | no | — |
| 208 | #1010 | — | 9 | 6 | no | — |
| 209 | #1010 | — | 9 | 2 | no | — |
| 210 | D3×#41 | — | 3 | 1 | no | — |
| 211 | D3×#41 | — | 9 | 1 | no | — |
| 212 | D3×#41 | — | 9 | 3 | no | — |
| 213 | D3×#41 | — | 9 | 3 | no | — |
| 214 | D3×#41 | — | 9 | 6 | no | — |
| 215 | D3×#41 | — | 9 | 6 | no | — |
| 216 | #1007 | — | 9 | 3 | no | — |
| 217 | #1007 | — | 9 | 3 | no | — |
| 218 | #1007 | — | 9 | 2 | no | — |
| 219 | #1007 | — | 9 | 2 | no | — |
| 220 | C2×D3×Q8 | — | 9 | 3 | no | — |
| 221 | C2×D3×Q8 | — | 9 | 3 | no | — |
| 222 | C2×D3×Q8 | — | 9 | 2 | no | — |
| 223 | C2×D3×Q8 | — | 9 | 2 | no | — |
| 224 | C2×D3×Q8 | — | 9 | 2 | no | — |
| 225 | C2×#237 | — | 9 | 6 | no | — |
| 226 | C2×#235 | — | 9 | 3 | no | — |
| 227 | C22×Dic6 | — | 9 | 3 | no | — |
| 228 | C22×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 229 | C22×C3×D3 | — | 3 | 3 | no | — |
| 230 | C2×D32 | — | 3 | 2 | no | — |
| 231 | C2×D32 | — | 3 | 2 | no | — |
| 232 | C32×Q8 | — | 2 | 1 | no | — |
| 233 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 234 | C32×Q8 | C22×D3 | 1 | 1 | yes | characteristic |
| 235 | C32×D4 | — | 2 | 3 | no | — |
| 236 | C32×D4 | C22×D3 | 1 | 3 | yes | — |
| 237 | C32×D4 | C22×D3 | 1 | 3 | yes | — |
| 238 | C2×C32×C4 | — | 2 | 3 | no | — |
| 239 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 240 | C2×C32×C4 | C22×D3 | 1 | 3 | yes | — |
| 241 | #638 | C22×D3 | 1 | 6 | yes | — |
| 242 | #638 | C22×D3 | 1 | 6 | yes | — |
| 243 | C2×C3⋊Dic3 | C22×D3 | 1 | 6 | yes | — |
| 244 | C2×C3⋊Dic3 | C22×D3 | 1 | 3 | yes | — |
| 245 | C4⋊(C3⋊D3) | C22×D3 | 1 | 3 | yes | — |
| 246 | C4⋊(C3⋊D3) | C22×D3 | 1 | 1 | yes | characteristic |
| 247 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 248 | C4×C3⋊D3 | C22×D3 | 1 | 6 | yes | — |
| 249 | C4×C3⋊D3 | C22×D3 | 1 | 1 | yes | characteristic |
| 250 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 251 | C4×C3⋊D3 | C22×D3 | 1 | 3 | yes | — |
| 252 | #634 | C22×D3 | 1 | 3 | yes | — |
| 253 | #634 | C22×D3 | 1 | 3 | yes | — |
| 254 | #634 | C22×D3 | 1 | 6 | yes | — |
| 255 | C3×#67 | — | 3 | 6 | no | — |
| 256 | C3×#67 | — | 3 | 6 | no | — |
| 257 | C3×#67 | — | 3 | 6 | no | — |
| 258 | C3×#67 | — | 3 | 6 | no | — |
| 259 | C3×#67 | — | 6 | 6 | no | — |
| 260 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 261 | C2×C3×Dic3 | — | 3 | 3 | no | — |
| 262 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 263 | C2×C3×Dic3 | — | 3 | 6 | no | — |
| 264 | C2×C3×Dic3 | — | 6 | 6 | no | — |
| 265 | C3×D12 | — | 3 | 3 | no | — |
| 266 | C3×D12 | — | 3 | 1 | no | — |
| 267 | C3×D12 | — | 3 | 1 | no | — |
| 268 | C3×D12 | — | 3 | 1 | no | — |
| 269 | C3×D12 | — | 6 | 1 | no | — |
| 270 | C3×C4×D3 | — | 3 | 1 | no | — |
| 271 | C3×C4×D3 | — | 3 | 3 | no | — |
| 272 | C3×C4×D3 | — | 3 | 3 | no | — |
| 273 | C3×C4×D3 | — | 3 | 3 | no | — |
| 274 | C3×C4×D3 | — | 3 | 6 | no | — |
| 275 | C3×C4×D3 | — | 3 | 6 | no | — |
| 276 | C3×C4×D3 | — | 3 | 6 | no | — |
| 277 | C3×C4×D3 | — | 6 | 6 | no | — |
| 278 | C3×Dic6 | — | 3 | 3 | no | — |
| 279 | C3×Dic6 | — | 3 | 6 | no | — |
| 280 | C3×Dic6 | — | 3 | 3 | no | — |
| 281 | C3×Dic6 | — | 3 | 3 | no | — |
| 282 | C3×Dic6 | — | 3 | 6 | no | — |
| 283 | C3×Dic6 | — | 3 | 6 | no | — |
| 284 | C3×Dic6 | — | 3 | 3 | no | — |
| 285 | C3×Dic6 | — | 6 | 3 | no | — |
| 286 | C3×Dic6 | — | 6 | 6 | no | — |
| 287 | #627 | — | 3 | 12 | no | — |
| 288 | #627 | — | 3 | 6 | no | — |
| 289 | #627 | — | 3 | 12 | no | — |
| 290 | #627 | — | 3 | 6 | no | — |
| 291 | #626 | — | 3 | 6 | no | — |
| 292 | #626 | — | 3 | 6 | no | — |
| 293 | #626 | — | 3 | 6 | no | — |
| 294 | #626 | — | 3 | 2 | no | — |
| 295 | #625 | — | 3 | 6 | no | — |
| 296 | #625 | — | 3 | 2 | no | — |
| 297 | #624 | — | 3 | 6 | no | — |
| 298 | #624 | — | 3 | 12 | no | — |
| 299 | #624 | — | 3 | 6 | no | — |
| 300 | D3×Dic3 | — | 3 | 6 | no | — |
| 301 | D3×Dic3 | — | 3 | 12 | no | — |
| 302 | D3×Dic3 | — | 3 | 6 | no | — |
| 303 | D3×Dic3 | — | 3 | 6 | no | — |
| 304 | D3×Dic3 | — | 3 | 6 | no | — |
| 305 | C2×2−1+4 | — | 27 | 1 | no | Sylow |
| 306 | C2×H(3,𝔽3) | — | 2 | 3 | no | — |
| 307 | C2×H(3,𝔽3) | C25 | 1 | 1 | yes | characteristic |
| 308 | #272 | — | 2 | 2 | no | — |
| 309 | (C3⋊D3)⋊C3 | — | 2 | 2 | no | — |
| 310 | (C3⋊D3)⋊C3 | — | 2 | 3 | no | — |
| 311 | (C3⋊D3)⋊C3 | 2−1+4 | 1 | 2 | yes | complemented |
| 312 | C3×#41 | — | 3 | 1 | no | — |
| 313 | C3×#41 | — | 3 | 1 | no | — |
| 314 | C3×#41 | — | 6 | 1 | no | — |
| 315 | C3×#41 | — | 9 | 3 | no | — |
| 316 | C3×#41 | — | 9 | 3 | no | — |
| 317 | C3×#41 | — | 9 | 6 | no | — |
| 318 | C3×#41 | — | 9 | 3 | no | — |
| 319 | C3×#41 | — | 9 | 1 | no | — |
| 320 | C3×#41 | — | 9 | 6 | no | — |
| 321 | C3×#41 | — | 9 | 3 | no | — |
| 322 | C3×#41 | D32 | 1 | 1 | yes | characteristic |
| 323 | C2×C3×Q8 | — | 9 | 3 | no | — |
| 324 | C2×C3×Q8 | — | 9 | 1 | no | — |
| 325 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 326 | C2×C3×Q8 | — | 9 | 2 | no | — |
| 327 | C2×C3×Q8 | — | 9 | 3 | no | — |
| 328 | C2×C3×D4 | — | 9 | 3 | no | — |
| 329 | C22×C3×C4 | — | 9 | 3 | no | — |
| 330 | C2×#67 | — | 9 | 6 | no | — |
| 331 | C22×Dic3 | — | 9 | 6 | no | — |
| 332 | #239 | — | 3 | 1 | no | — |
| 333 | #239 | — | 9 | 1 | no | — |
| 334 | #239 | — | 9 | 3 | no | — |
| 335 | #239 | — | 9 | 6 | no | — |
| 336 | #239 | — | 9 | 6 | no | — |
| 337 | #239 | — | 9 | 3 | no | — |
| 338 | D3×Q8 | — | 3 | 2 | no | — |
| 339 | D3×Q8 | — | 3 | 2 | no | — |
| 340 | D3×Q8 | — | 3 | 1 | no | — |
| 341 | D3×Q8 | — | 3 | 2 | no | — |
| 342 | D3×Q8 | — | 6 | 2 | no | — |
| 343 | D3×Q8 | — | 9 | 1 | no | — |
| 344 | D3×Q8 | — | 9 | 2 | no | — |
| 345 | D3×Q8 | — | 9 | 3 | no | — |
| 346 | D3×Q8 | — | 9 | 6 | no | — |
| 347 | D3×Q8 | — | 9 | 6 | no | — |
| 348 | D3×Q8 | — | 9 | 6 | no | — |
| 349 | D3×Q8 | — | 9 | 6 | no | — |
| 350 | D3×Q8 | — | 9 | 3 | no | — |
| 351 | D3×Q8 | — | 9 | 6 | no | — |
| 352 | D3×Q8 | — | 9 | 6 | no | — |
| 353 | D3×Q8 | — | 9 | 6 | no | — |
| 354 | D3×Q8 | — | 9 | 6 | no | — |
| 355 | D3×Q8 | — | 9 | 6 | no | — |
| 356 | D3×Q8 | — | 9 | 6 | no | — |
| 357 | #237 | — | 3 | 6 | no | — |
| 358 | #237 | — | 3 | 6 | no | — |
| 359 | #237 | — | 3 | 3 | no | — |
| 360 | #237 | — | 3 | 6 | no | — |
| 361 | #237 | — | 6 | 6 | no | — |
| 362 | #237 | — | 9 | 6 | no | — |
| 363 | #237 | — | 9 | 3 | no | — |
| 364 | #237 | — | 9 | 3 | no | — |
| 365 | #237 | — | 9 | 6 | no | — |
| 366 | #237 | — | 9 | 3 | no | — |
| 367 | #237 | — | 9 | 6 | no | — |
| 368 | #237 | — | 9 | 12 | no | — |
| 369 | #237 | — | 9 | 6 | no | — |
| 370 | #237 | — | 9 | 12 | no | — |
| 371 | #237 | — | 9 | 12 | no | — |
| 372 | #237 | — | 9 | 12 | no | — |
| 373 | #237 | — | 9 | 6 | no | — |
| 374 | D3×D4 | — | 3 | 3 | no | — |
| 375 | D3×D4 | — | 9 | 3 | no | — |
| 376 | D3×D4 | — | 9 | 1 | no | — |
| 377 | D3×D4 | — | 9 | 1 | no | — |
| 378 | D3×D4 | — | 9 | 6 | no | — |
| 379 | D3×D4 | — | 9 | 6 | no | — |
| 380 | #235 | — | 3 | 3 | no | — |
| 381 | #235 | — | 3 | 3 | no | — |
| 382 | #235 | — | 3 | 3 | no | — |
| 383 | #235 | — | 3 | 3 | no | — |
| 384 | #235 | — | 6 | 3 | no | — |
| 385 | #235 | — | 9 | 3 | no | — |
| 386 | #235 | — | 9 | 3 | no | — |
| 387 | #235 | — | 9 | 6 | no | — |
| 388 | #235 | — | 9 | 3 | no | — |
| 389 | #235 | — | 9 | 6 | no | — |
| 390 | #235 | — | 9 | 6 | no | — |
| 391 | #235 | — | 9 | 6 | no | — |
| 392 | #235 | — | 9 | 6 | no | — |
| 393 | #235 | — | 9 | 3 | no | — |
| 394 | #235 | — | 9 | 12 | no | — |
| 395 | #235 | — | 9 | 6 | no | — |
| 396 | #235 | — | 9 | 12 | no | — |
| 397 | C2×D12 | — | 9 | 1 | no | — |
| 398 | C2×C4×D3 | — | 3 | 3 | no | — |
| 399 | C2×C4×D3 | — | 9 | 3 | no | — |
| 400 | C2×C4×D3 | — | 9 | 6 | no | — |
| 401 | C2×C4×D3 | — | 9 | 6 | no | — |
| 402 | C2×C4×D3 | — | 9 | 6 | no | — |
| 403 | C2×C4×D3 | — | 9 | 6 | no | — |
| 404 | C2×C4×D3 | — | 9 | 6 | no | — |
| 405 | C2×Dic6 | — | 3 | 3 | no | — |
| 406 | C2×Dic6 | — | 3 | 3 | no | — |
| 407 | C2×Dic6 | — | 3 | 3 | no | — |
| 408 | C2×Dic6 | — | 6 | 3 | no | — |
| 409 | C2×Dic6 | — | 9 | 3 | no | — |
| 410 | C2×Dic6 | — | 9 | 6 | no | — |
| 411 | C2×Dic6 | — | 9 | 3 | no | — |
| 412 | C2×Dic6 | — | 9 | 6 | no | — |
| 413 | C2×Dic6 | — | 9 | 6 | no | — |
| 414 | C2×Dic6 | — | 9 | 6 | no | — |
| 415 | C2×Dic6 | — | 9 | 6 | no | — |
| 416 | C2×Dic6 | — | 9 | 6 | no | — |
| 417 | C2×Dic6 | — | 9 | 6 | no | — |
| 418 | C2×Dic6 | — | 9 | 6 | no | — |
| 419 | C22×C32 | — | 2 | 3 | no | — |
| 420 | C22×C32 | C23×D3 | 1 | 3 | yes | — |
| 421 | C22×C32 | C23×D3 | 1 | 3 | yes | — |
| 422 | C2×C3⋊D3 | — | 2 | 6 | no | — |
| 423 | C2×C3⋊D3 | C23×D3 | 1 | 3 | yes | — |
| 424 | C2×C3⋊D3 | C23×D3 | 1 | 2 | yes | — |
| 425 | C2×C3⋊D3 | C23×D3 | 1 | 1 | yes | characteristic |
| 426 | C2×C3×D3 | — | 3 | 1 | no | — |
| 427 | C2×C3×D3 | — | 3 | 3 | no | — |
| 428 | C2×C3×D3 | — | 3 | 2 | no | — |
| 429 | C2×C3×D3 | — | 3 | 2 | no | — |
| 430 | C2×C3×D3 | — | 3 | 2 | no | — |
| 431 | C2×C3×D3 | — | 6 | 2 | no | — |
| 432 | C2×C3×D3 | — | 6 | 6 | no | — |
| 433 | D32 | — | 6 | 4 | no | — |
| 434 | D32 | — | 6 | 4 | no | — |
| 435 | C32×C4 | — | 2 | 1 | no | — |
| 436 | C32×C4 | — | 2 | 3 | no | — |
| 437 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 438 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 439 | C32×C4 | C23×D3 | 1 | 1 | yes | characteristic |
| 440 | C32×C4 | C23×D3 | 1 | 3 | yes | — |
| 441 | C3⋊Dic3 | C23×D3 | 1 | 6 | yes | — |
| 442 | C3⋊Dic3 | C23×D3 | 1 | 3 | yes | — |
| 443 | C3⋊Dic3 | C23×D3 | 1 | 1 | yes | characteristic |
| 444 | C3×Dic3 | — | 3 | 3 | no | — |
| 445 | C3×Dic3 | — | 3 | 6 | no | — |
| 446 | C3×Dic3 | — | 3 | 1 | no | — |
| 447 | C3×Dic3 | — | 3 | 6 | no | — |
| 448 | C3×Dic3 | — | 3 | 6 | no | — |
| 449 | C3×Dic3 | — | 6 | 6 | no | — |
| 450 | 2−1+4 | — | 9 | 1 | no | — |
| 451 | 2−1+4 | — | 9 | 1 | no | — |
| 452 | 2−1+4 | — | 27 | 2 | no | — |
| 453 | 2−1+4 | — | 27 | 3 | no | — |
| 454 | 2−1+4 | — | 27 | 3 | no | — |
| 455 | 2−1+4 | — | 27 | 6 | no | — |
| 456 | C2×#41 | — | 9 | 1 | no | — |
| 457 | C2×#41 | — | 27 | 3 | no | — |
| 458 | C2×#41 | — | 27 | 6 | no | — |
| 459 | C22×Q8 | — | 27 | 3 | no | — |
| 460 | C22×Q8 | — | 27 | 2 | no | — |
| 461 | H(3,𝔽3) | C2×2−1+4 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 462 | C23×C3 | — | 9 | 3 | no | — |
| 463 | C22×D3 | — | 3 | 3 | no | — |
| 464 | C22×D3 | — | 9 | 3 | no | — |
| 465 | C22×D3 | — | 9 | 2 | no | — |
| 466 | C22×D3 | — | 9 | 2 | no | — |
| 467 | C22×D3 | — | 9 | 2 | no | — |
| 468 | C3×Q8 | — | 3 | 1 | no | — |
| 469 | C3×Q8 | — | 3 | 1 | no | — |
| 470 | C3×Q8 | — | 6 | 1 | no | — |
| 471 | C3×Q8 | — | 9 | 3 | no | — |
| 472 | C3×Q8 | — | 9 | 3 | no | — |
| 473 | C3×Q8 | — | 9 | 6 | no | — |
| 474 | C3×Q8 | — | 9 | 6 | no | — |
| 475 | C3×Q8 | — | 9 | 3 | no | — |
| 476 | C3×Q8 | C2×D32 | 1 | 1 | yes | characteristic |
| 477 | C3×D4 | — | 3 | 3 | no | — |
| 478 | C3×D4 | — | 3 | 3 | no | — |
| 479 | C3×D4 | — | 6 | 3 | no | — |
| 480 | C3×D4 | — | 9 | 1 | no | — |
| 481 | C3×D4 | — | 9 | 3 | no | — |
| 482 | C3×D4 | — | 9 | 6 | no | — |
| 483 | C3×D4 | — | 9 | 6 | no | — |
| 484 | C3×D4 | — | 9 | 6 | no | — |
| 485 | C3×D4 | — | 9 | 1 | no | — |
| 486 | C3×D4 | C2×D32 | 1 | 3 | yes | — |
| 487 | C2×C3×C4 | — | 3 | 3 | no | — |
| 488 | C2×C3×C4 | — | 3 | 3 | no | — |
| 489 | C2×C3×C4 | — | 6 | 3 | no | — |
| 490 | C2×C3×C4 | — | 9 | 1 | no | — |
| 491 | C2×C3×C4 | — | 9 | 3 | no | — |
| 492 | C2×C3×C4 | — | 9 | 3 | no | — |
| 493 | C2×C3×C4 | — | 9 | 3 | no | — |
| 494 | C2×C3×C4 | — | 9 | 6 | no | — |
| 495 | C2×C3×C4 | — | 9 | 3 | no | — |
| 496 | C2×C3×C4 | — | 9 | 6 | no | — |
| 497 | C2×C3×C4 | — | 9 | 6 | no | — |
| 498 | C2×C3×C4 | — | 9 | 6 | no | — |
| 499 | C2×C3×C4 | C2×D32 | 1 | 3 | yes | — |
| 500 | #67 | — | 3 | 6 | no | — |
| 501 | #67 | — | 3 | 6 | no | — |
| 502 | #67 | — | 3 | 6 | no | — |
| 503 | #67 | — | 3 | 6 | no | — |
| 504 | #67 | — | 6 | 6 | no | — |
| 505 | #67 | — | 9 | 6 | no | — |
| 506 | #67 | — | 9 | 6 | no | — |
| 507 | #67 | — | 9 | 6 | no | — |
| 508 | #67 | — | 9 | 2 | no | — |
| 509 | #67 | — | 9 | 6 | no | — |
| 510 | #67 | — | 9 | 6 | no | — |
| 511 | #67 | — | 9 | 2 | no | — |
| 512 | #67 | — | 9 | 6 | no | — |
| 513 | C2×Dic3 | — | 3 | 6 | no | — |
| 514 | C2×Dic3 | — | 3 | 6 | no | — |
| 515 | C2×Dic3 | — | 3 | 6 | no | — |
| 516 | C2×Dic3 | — | 3 | 3 | no | — |
| 517 | C2×Dic3 | — | 6 | 6 | no | — |
| 518 | C2×Dic3 | — | 9 | 3 | no | — |
| 519 | C2×Dic3 | — | 9 | 6 | no | — |
| 520 | C2×Dic3 | — | 9 | 6 | no | — |
| 521 | C2×Dic3 | — | 9 | 6 | no | — |
| 522 | C2×Dic3 | — | 9 | 6 | no | — |
| 523 | C2×Dic3 | — | 9 | 12 | no | — |
| 524 | D12 | — | 3 | 1 | no | — |
| 525 | D12 | — | 3 | 1 | no | — |
| 526 | D12 | — | 3 | 1 | no | — |
| 527 | D12 | — | 3 | 3 | no | — |
| 528 | D12 | — | 6 | 1 | no | — |
| 529 | D12 | — | 9 | 1 | no | — |
| 530 | D12 | — | 9 | 3 | no | — |
| 531 | D12 | — | 9 | 6 | no | — |
| 532 | D12 | — | 9 | 2 | no | — |
| 533 | D12 | — | 9 | 6 | no | — |
| 534 | C4×D3 | — | 3 | 6 | no | — |
| 535 | C4×D3 | — | 3 | 6 | no | — |
| 536 | C4×D3 | — | 3 | 1 | no | — |
| 537 | C4×D3 | — | 3 | 3 | no | — |
| 538 | C4×D3 | — | 3 | 3 | no | — |
| 539 | C4×D3 | — | 3 | 3 | no | — |
| 540 | C4×D3 | — | 3 | 6 | no | — |
| 541 | C4×D3 | — | 6 | 6 | no | — |
| 542 | C4×D3 | — | 9 | 1 | no | — |
| 543 | C4×D3 | — | 9 | 3 | no | — |
| 544 | C4×D3 | — | 9 | 6 | no | — |
| 545 | C4×D3 | — | 9 | 3 | no | — |
| 546 | C4×D3 | — | 9 | 3 | no | — |
| 547 | C4×D3 | — | 9 | 6 | no | — |
| 548 | C4×D3 | — | 9 | 12 | no | — |
| 549 | C4×D3 | — | 9 | 6 | no | — |
| 550 | C4×D3 | — | 9 | 6 | no | — |
| 551 | C4×D3 | — | 9 | 6 | no | — |
| 552 | C4×D3 | — | 9 | 12 | no | — |
| 553 | C4×D3 | — | 9 | 6 | no | — |
| 554 | C4×D3 | — | 9 | 6 | no | — |
| 555 | Dic6 | — | 3 | 3 | no | — |
| 556 | Dic6 | — | 3 | 3 | no | — |
| 557 | Dic6 | — | 3 | 6 | no | — |
| 558 | Dic6 | — | 3 | 6 | no | — |
| 559 | Dic6 | — | 3 | 3 | no | — |
| 560 | Dic6 | — | 3 | 6 | no | — |
| 561 | Dic6 | — | 3 | 3 | no | — |
| 562 | Dic6 | — | 6 | 3 | no | — |
| 563 | Dic6 | — | 6 | 6 | no | — |
| 564 | Dic6 | — | 9 | 3 | no | — |
| 565 | Dic6 | — | 9 | 6 | no | — |
| 566 | Dic6 | — | 9 | 3 | no | — |
| 567 | Dic6 | — | 9 | 12 | no | — |
| 568 | Dic6 | — | 9 | 6 | no | — |
| 569 | Dic6 | — | 9 | 6 | no | — |
| 570 | Dic6 | — | 9 | 12 | no | — |
| 571 | Dic6 | — | 9 | 12 | no | — |
| 572 | Dic6 | — | 9 | 6 | no | — |
| 573 | C2×C32 | — | 2 | 3 | no | — |
| 574 | C2×C32 | — | 2 | 3 | no | — |
| 575 | C2×C32 | — | 2 | 1 | no | — |
| 576 | C2×C32 | — | 4 | 3 | no | — |
| 577 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 578 | C2×C32 | C24×D3 | 1 | 1 | yes | characteristic |
| 579 | C3⋊D3 | — | 2 | 3 | no | — |
| 580 | C3⋊D3 | — | 2 | 2 | no | — |
| 581 | C3⋊D3 | #1010 | 1 | 2 | yes | complemented |
| 582 | C3×D3 | — | 3 | 2 | no | — |
| 583 | C3×D3 | — | 6 | 2 | no | — |
| 584 | C3×D3 | — | 6 | 2 | no | — |
| 585 | C3×D3 | — | 6 | 3 | no | — |
| 586 | C3×D3 | — | 6 | 2 | no | — |
| 587 | C3×D3 | — | 12 | 2 | no | — |
| 588 | #41 | — | 9 | 1 | no | — |
| 589 | #41 | — | 9 | 3 | no | — |
| 590 | #41 | — | 9 | 6 | no | — |
| 591 | #41 | — | 9 | 6 | no | — |
| 592 | #41 | — | 9 | 3 | no | — |
| 593 | #41 | — | 9 | 3 | no | — |
| 594 | #41 | — | 9 | 3 | no | — |
| 595 | #41 | — | 27 | 6 | no | — |
| 596 | #41 | — | 27 | 6 | no | — |
| 597 | #41 | — | 27 | 12 | no | — |
| 598 | #41 | — | 27 | 12 | no | — |
| 599 | #41 | — | 27 | 3 | no | — |
| 600 | #41 | — | 27 | 3 | no | — |
| 601 | #41 | — | 27 | 6 | no | — |
| 602 | #41 | — | 27 | 6 | no | — |
| 603 | #41 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic, complemented |
| 604 | C2×Q8 | — | 9 | 1 | no | — |
| 605 | C2×Q8 | — | 9 | 2 | no | — |
| 606 | C2×Q8 | — | 9 | 2 | no | — |
| 607 | C2×Q8 | — | 9 | 3 | no | — |
| 608 | C2×Q8 | — | 9 | 3 | no | — |
| 609 | C2×Q8 | — | 27 | 6 | no | — |
| 610 | C2×Q8 | — | 27 | 3 | no | — |
| 611 | C2×Q8 | — | 27 | 6 | no | — |
| 612 | C2×Q8 | — | 27 | 6 | no | — |
| 613 | C2×Q8 | — | 27 | 6 | no | — |
| 614 | C2×Q8 | — | 27 | 6 | no | — |
| 615 | C2×Q8 | — | 27 | 6 | no | — |
| 616 | C2×D4 | — | 9 | 3 | no | — |
| 617 | C2×D4 | — | 27 | 1 | no | — |
| 618 | C2×D4 | — | 27 | 6 | no | — |
| 619 | C22×C4 | — | 9 | 3 | no | — |
| 620 | C22×C4 | — | 27 | 6 | no | — |
| 621 | C22×C4 | — | 27 | 6 | no | — |
| 622 | C22×C3 | — | 3 | 3 | no | — |
| 623 | C22×C3 | — | 3 | 3 | no | — |
| 624 | C22×C3 | — | 6 | 3 | no | — |
| 625 | C22×C3 | — | 9 | 1 | no | — |
| 626 | C22×C3 | — | 9 | 3 | no | — |
| 627 | C22×C3 | — | 9 | 2 | no | — |
| 628 | C22×C3 | — | 9 | 2 | no | — |
| 629 | C22×C3 | — | 18 | 6 | no | — |
| 630 | C22×C3 | C22×D32 | 1 | 3 | yes | — |
| 631 | C2×D3 | — | 3 | 1 | no | — |
| 632 | C2×D3 | — | 3 | 2 | no | — |
| 633 | C2×D3 | — | 3 | 2 | no | — |
| 634 | C2×D3 | — | 3 | 2 | no | — |
| 635 | C2×D3 | — | 3 | 3 | no | — |
| 636 | C2×D3 | — | 6 | 2 | no | — |
| 637 | C2×D3 | — | 6 | 6 | no | — |
| 638 | C2×D3 | — | 9 | 1 | no | — |
| 639 | C2×D3 | — | 9 | 3 | no | — |
| 640 | C2×D3 | — | 9 | 2 | no | — |
| 641 | C2×D3 | — | 18 | 6 | no | — |
| 642 | C2×D3 | — | 18 | 4 | no | — |
| 643 | C2×D3 | — | 18 | 4 | no | — |
| 644 | C2×D3 | — | 18 | 4 | no | — |
| 645 | C3×C4 | — | 3 | 1 | no | — |
| 646 | C3×C4 | — | 3 | 1 | no | — |
| 647 | C3×C4 | — | 3 | 3 | no | — |
| 648 | C3×C4 | — | 3 | 3 | no | — |
| 649 | C3×C4 | — | 6 | 1 | no | — |
| 650 | C3×C4 | — | 6 | 3 | no | — |
| 651 | C3×C4 | — | 9 | 1 | no | — |
| 652 | C3×C4 | — | 9 | 3 | no | — |
| 653 | C3×C4 | — | 9 | 6 | no | — |
| 654 | C3×C4 | — | 9 | 6 | no | — |
| 655 | C3×C4 | C22×D32 | 1 | 3 | yes | — |
| 656 | C3×C4 | C22×D32 | 1 | 1 | yes | characteristic |
| 657 | Dic3 | — | 3 | 6 | no | — |
| 658 | Dic3 | — | 3 | 6 | no | — |
| 659 | Dic3 | — | 3 | 6 | no | — |
| 660 | Dic3 | — | 3 | 3 | no | — |
| 661 | Dic3 | — | 3 | 1 | no | — |
| 662 | Dic3 | — | 6 | 6 | no | — |
| 663 | Dic3 | — | 9 | 1 | no | — |
| 664 | Dic3 | — | 9 | 3 | no | — |
| 665 | Dic3 | — | 9 | 6 | no | — |
| 666 | C32 | — | 2 | 1 | no | — |
| 667 | C32 | C2×#1010 | 1 | 1 | yes | characteristic, complemented |
| 668 | C32 | D3×2−1+4 | 1 | 1 | yes | characteristic, complemented |
| 669 | C23 | — | 9 | 3 | no | — |
| 670 | C23 | — | 27 | 2 | no | — |
| 671 | Q8 | — | 9 | 6 | no | — |
| 672 | Q8 | — | 9 | 3 | no | — |
| 673 | Q8 | — | 9 | 6 | no | — |
| 674 | Q8 | — | 9 | 3 | no | — |
| 675 | Q8 | — | 9 | 3 | no | — |
| 676 | Q8 | — | 27 | 6 | no | — |
| 677 | Q8 | — | 27 | 12 | no | — |
| 678 | Q8 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 679 | D4 | — | 9 | 6 | no | — |
| 680 | D4 | — | 9 | 6 | no | — |
| 681 | D4 | — | 9 | 6 | no | — |
| 682 | D4 | — | 9 | 3 | no | — |
| 683 | D4 | — | 9 | 1 | no | — |
| 684 | D4 | — | 9 | 1 | no | — |
| 685 | D4 | — | 27 | 2 | no | — |
| 686 | D4 | — | 27 | 6 | no | — |
| 687 | D4 | — | 27 | 6 | no | — |
| 688 | D4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 689 | C2×C4 | — | 9 | 3 | no | — |
| 690 | C2×C4 | — | 9 | 6 | no | — |
| 691 | C2×C4 | — | 9 | 6 | no | — |
| 692 | C2×C4 | — | 9 | 1 | no | — |
| 693 | C2×C4 | — | 9 | 3 | no | — |
| 694 | C2×C4 | — | 9 | 3 | no | — |
| 695 | C2×C4 | — | 9 | 3 | no | — |
| 696 | C2×C4 | — | 9 | 6 | no | — |
| 697 | C2×C4 | — | 9 | 6 | no | — |
| 698 | C2×C4 | — | 27 | 6 | no | — |
| 699 | C2×C4 | — | 27 | 6 | no | — |
| 700 | C2×C4 | — | 27 | 6 | no | — |
| 701 | C2×C4 | — | 27 | 12 | no | — |
| 702 | C2×C4 | C2×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 703 | C2×C3 | — | 2 | 3 | no | — |
| 704 | C2×C3 | — | 3 | 1 | no | — |
| 705 | C2×C3 | — | 3 | 1 | no | — |
| 706 | C2×C3 | — | 6 | 3 | no | — |
| 707 | C2×C3 | — | 6 | 3 | no | — |
| 708 | C2×C3 | — | 6 | 1 | no | — |
| 709 | C2×C3 | — | 9 | 2 | no | — |
| 710 | C2×C3 | — | 12 | 3 | no | — |
| 711 | C2×C3 | — | 18 | 2 | no | — |
| 712 | C2×C3 | — | 18 | 3 | no | — |
| 713 | C2×C3 | — | 18 | 2 | no | — |
| 714 | C2×C3 | C23×D32 | 1 | 1 | yes | characteristic |
| 715 | D3 | — | 3 | 2 | no | — |
| 716 | D3 | — | 6 | 2 | no | — |
| 717 | D3 | — | 6 | 2 | no | — |
| 718 | D3 | — | 6 | 3 | no | — |
| 719 | D3 | — | 6 | 2 | no | — |
| 720 | D3 | — | 9 | 2 | no | — |
| 721 | D3 | — | 12 | 2 | no | — |
| 722 | D3 | — | 18 | 3 | no | — |
| 723 | D3 | — | 18 | 2 | no | — |
| 724 | C22 | — | 9 | 1 | no | — |
| 725 | C22 | — | 9 | 2 | no | — |
| 726 | C22 | — | 9 | 2 | no | — |
| 727 | C22 | — | 9 | 3 | no | — |
| 728 | C22 | — | 18 | 6 | no | — |
| 729 | C22 | — | 54 | 4 | no | — |
| 730 | C22 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 731 | C4 | — | 9 | 1 | no | — |
| 732 | C4 | — | 9 | 3 | no | — |
| 733 | C4 | — | 9 | 6 | no | — |
| 734 | C4 | — | 9 | 6 | no | — |
| 735 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 3 | yes | — |
| 736 | C4 | C22×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 737 | C3 | — | 3 | 1 | no | — |
| 738 | C3 | — | 3 | 1 | no | — |
| 739 | C3 | — | 6 | 1 | no | — |
| 740 | C3 | D3×#1010 | 1 | 1 | yes | characteristic |
| 741 | C2 | — | 2 | 3 | no | — |
| 742 | C2 | — | 9 | 2 | no | — |
| 743 | C2 | — | 18 | 3 | no | — |
| 744 | C2 | — | 18 | 2 | no | — |
| 745 | C2 | — | 18 | 2 | no | — |
| 746 | C2 | C23×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #11722676 | C2 | semidirect |
| 2. #11722639 | C2 | semidirect |
| 3. #41×(C3⋊D3)⋊C3 | C2 | semidirect |
| 4. Q8×((C3⋊D3)⋊C3)⋊C2 | C2 | semidirect |
| 5. #11722516 | C2 | semidirect |
| 6. #11722504 | C2 | semidirect |
| 7. #11722502 | C2 | semidirect |
| 8. #11722490 | C2 | semidirect |
| 9. #11722483 | C2 | semidirect |
| 10. #11722482 | C2 | semidirect |
| 11. C2×((C3⋊D3)⋊C3)⋊Q8 | C2 | semidirect |
| 14. #41×H(3,𝔽3) | C22 | semidirect |
| 15. Q8×#272 | C22 | semidirect |
| 16. #88744 | C22 | semidirect |
| 17. #88740 | C22 | semidirect |
| 18. C2×#6229 | C22 | semidirect |
| 19. #88722 | C22 | semidirect |
| 21. Q8×(C3⋊D3)⋊C3 | C22 | semidirect |
| 22. #3830⋊C3 | C22 | semidirect |
| 23. #3830⋊C3 | C22 | semidirect |
| 25. #3828⋊C3 | C22 | semidirect |
| 26. #3828⋊C3 | C22 | semidirect |
| 28. C2×#634⋊C3 | C22 | semidirect |
| 30. #88672 | C22 | semidirect |
| 31. #88671 | C22 | semidirect |
| 32. #88671 | C22 | semidirect |
| 34. C2×#6196 | C22 | semidirect |
| 37. #88652 | C22 | semidirect |
| 38. #88651 | C22 | semidirect |
| 39. #88650 | C22 | semidirect |
| 40. #88649 | C22 | semidirect |
| 41. #88648 | C22 | semidirect |
| 42. #88648 | C22 | semidirect |
| 45. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 46. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 47. ((C3⋊D3)⋊C3)⋊Q8 | C22 | semidirect |
| 48. #64367 | D3 | semidirect |
| 49. #41×C3⋊D3 | D3 | semidirect |
| 109. C32×#41 | C2×D3 | semidirect |
| 110. C32×#41 | C2×D3 | semidirect |
| 111. #3832 | C2×D3 | semidirect |
| 113. Q8×C3⋊D3 | C2×D3 | semidirect |
| 114. #3830 | C2×D3 | semidirect |
| 115. #3830 | C2×D3 | semidirect |
| 117. #3828 | C2×D3 | semidirect |
| 118. #3828 | C2×D3 | semidirect |
| 120. C2×#634 | C2×D3 | semidirect |
| 311. (C3⋊D3)⋊C3 | 2−1+4 | semidirect |
| 461. H(3,𝔽3) | C2×2−1+4 | semidirect |
| 581. C3⋊D3 | #1010 | semidirect |
| 603. #41 | ((C3⋊D3)⋊C3)⋊C2 | semidirect |
| 667. C32 | C2×#1010 | semidirect |
| 668. C32 | D3×2−1+4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11722676 | 2 |
| #11722639 | 2 |
| #41×(C3⋊D3)⋊C3 | 2 |
| Q8×((C3⋊D3)⋊C3)⋊C2 | 2 |
| #11722516 | 2 |
| #11722504 | 2 |
| #11722502 | 2 |
| #11722490 | 2 |
| #11722483 | 2 |
| #11722482 | 2 |
| C2×((C3⋊D3)⋊C3)⋊Q8 | 2 |
| #10596694 | 3 |
| D3×#1010 | 3 |